Description

There are $n$ residential areas in the kingdom. They are connected by $n - 1$ roads, and it is guaranteed that from any residential area you can reach any other one. The length of each road is $1$.

In every residential area except area $1$, there lives a little penguin. One day, a cat starts from residential area $1$ and wants to visit some penguins. However, the cat is very lazy and is only willing to visit penguins whose distance from it is at most $d$.

Please tell the cat how many penguins it can visit.

Input Format

The first line contains two integers $n, d$, with the meanings as described above.

Starting from the second line, there are $n - 1$ lines. Each line contains two integers $u, v$, indicating that there is a road between residential areas $u$ and $v$.

Output Format

Output one integer in a single line, indicating how many penguins the cat can visit.

5 1
1 2
1 3
2 4
3 5

2

Hint

For $100\%$ of the testdata, $1 \le n, d \le 10^5$. It is guaranteed that all residential areas are numbered starting from $1$.

Translated by ChatGPT 5